I recommend buying the tickets online on
www.bahn.de. If you chose a normalpreis ticket you can take any connection, so there is no problem with delayed flights in this case. In addition they don't have to worry about using the ticket machines, which are not really that trivial to use for people not used to them. In addition, booking on
www.bahn.de you can buy one ticket for the while trip. Otherwise, your parents would have to buy a regional (VVS) ticket to Stuttgart Hauptbahnhof on the ticket machine (there's no human help available) and get a second ticket for the train once they have arrived at Hauptbahnhof. This will add time and stress.